This is a premium problem. We're working on making it available for free soon.
Explore Free ProblemsUse these hints if you're stuck. Try solving on your own first.
How does the GCD of an array change when you add more elements to a subarray?
The GCD will always decrease when increasing the size of the subarray,
Keep adding elements to a subarray and if adding a new element will make the GCD = 1, add a new split and a new subarray.
Solutions for this premium problem will be available for free soon.
Browse Free ProblemsWatch expert explanations and walkthroughs
Jot down your thoughts, approach, and key learnings
Prime factorization helps determine whether consecutive elements can share a common divisor greater than one. If two numbers share at least one prime factor, they can belong to the same valid subarray with GCD greater than one.
Problems involving GCD, prime factors, and dynamic programming are common in technical interviews. Variants of this question test number theory insights and the ability to optimize array partitioning using efficient data structures.
A hash map or dictionary is commonly used to store the last best split count for each prime factor. This structure allows constant-time lookups and updates while iterating through the array and processing factors.
The optimal approach combines dynamic programming with prime factor tracking. For each number, compute its prime factors and maintain the minimum split count associated with those factors. This allows efficient updates and avoids recomputing GCDs across many subarrays.
